Soldiers Rifle
Do soldiers rifles return home with the unit in the US army?
When a unit has finished its service does it return home with its equipment and rifles (m16s)?
Both of the other answers are only partially correct, and don't really answer your question. In fact the one mentioning the C-21 (a military Lear Jet) might even be sarcastic in nature.
I'll use Iraq as an example, bit not go into too much esoteric military terminology: when we first invaded, some units were able to deploy without most of their equipment and fall in on prepositioned vehicles and certain other equipment. These units normally brought their radios, computers, rifles, machine guns, etc - the small stuff. The large equipment such as tanks, APCs, trucks, generators, and so on were there in large motor pools waiting on a unit to show up and draw the gear. Other units had all their gear packed onto ships and sent over. A very small amount of vehicles might be authorized for both groups to fly over from what they had stateside or in Europe. Sometimes these exceptions were unit pimped-out communications / headquarters vehicles or some new piece of large equipment.
Almost without exception, when a unit redeployed back to home station, all of their large equipment was left in place for the next unit to take over. This included the equipment they drew out of prepositioned stocks, and the large equipment that was shipped over in units that showed up with all their own stuff. Units would go home with any specialized equipment they brought over, weapons, and Soldier's personal gear.
For example, my MiTT team deployed with our personal gear, our personal weapons (rifles and pistols), and some new electronics that had just been issued. When we arrived we took over the vehicles, generators, sat dish, personal comms devices, crew-served weapons, and so on. When we left, we turned over to our replacements everything, to include the new electronic devices we had deployed with. We only went back with out personal gear and weapons. This is how most units have done it.
With the current draw down in Iraq, as a combat unit would go home, the troops took their personal gear and weapons, and would turn-in everything else to logistic collection points, where the logisticians would determine if the equipment was going back stateside, going to Afghanistan, given to the locals, or sold under foreign military sales.